In each scenario, the goal is to find the factor or rate increase from a starting value to a final value.

Scenario 1)

Suppose you currently have five dollars in the bank. Tomorrow, you deposit (that is add) ten dollars to your account. This gives you a total of fifteen dollars in your account. By what factor or rate did your account increase compared to yesterday?

The accounts value increased by a factor of 3 because 15 divided by 5 = 3. Or, in order to answer any similar problem, once can simply use the following equation:

So, what were to happen if we start the initial value, 'z' at 0? Since any number divided by 0 is 0, this would return an incorrect value for x.

Scenario 2)

Your account currently has 0 dollars but you add five dollars. By what factor did your account increase?

x = 0 / 5x = 0

As long as you don't start with 0, the pattern holds just fine. For any x greater than 0, one can computer a factor increase (or decrease) at the bank, but not when you start at 0.

So, my question is not why 0/ x = 0 but instead why this implies my bank account did not increase when surely it did. I give this conclusion because a factor of 0 increase means my account did not change - yet it did! Now, by how much?

Is it possible to know by what factor my account increases? Or is this simply the wrong question to ask?

greenknight_v wrote:So, what were to happen if we start the initial value, 'z' at 0?

Since you are trying to find a "factor", and since "factors" apply to multiplication, and since multiplying zero by anything will give you zero, obviously the concept of "increasing by some factor" won't apply when the original value was zero.

greenknight_v wrote:Ok, but what is the meaning of multiplication? It is simply another form of addition (I think).

Yes. But once you go to that other "form", you get different rules, different terms, and different tools. You are asking "how many times is (this) of (that), when (that) equals zero?" The question makes no sense in context.